The invention relates generally to better devices for improvements in a two-photon absorptive switch and for improvements in stability for single or interconnected interferometers. In particular, the invention incorporates a non-critically phase-matched (NCPM) crystal to improve the performance of a two-photon absorption (TPA) switch. Additionally, the invention incorporates monolithic optics to improve the stability of Mach-Zehnder Interferometer (MZI) devices.
Quantum optic interference can be compromised under two-slit conditions by which-path information of photons within an experimental apparatus, the identity of the path taken by the photon being known as complete “which-path” information. It is desirable that an Einstein-Podolsky-Rosen (EPR) state (e.g., a “two-photon” quantum state) remains free from which-path information. The EPR state originated with a gedanken challenge posed to quantum mechanics in its formative years regarding completeness by A. Einstein, B. Podolsky and N. Rosen in “Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?”, Phys. Rev. 47 (1935) 777-780, to which N. Bohr responded the following year in an article of the same title in Phys. Rev. 48 (1936) 696-702.
Einstein had contemplated that local realism as spatial separation of two systems cannot influence one another because a mediating influence is bound by locality (relativistic laws) and hence there can be no causality (cause and effect) between the two systems. Subsequently, J. S. Bell restated this assertion in “On the Einstein Podolsky Rosen Paradox”, Physics 1 (1964) 195-200 demonstrating that local realism as contemplated by Einstein yields an algebraic prediction called Bell's inequality, which involves hidden variables that could potentially complete quantum mechanics. However, Bell's inequality is violated by predictions of quantum mechanics. Thus, local realism cannot be used to complete quantum mechanics.
Bell's theorem was further refined for experimental practicality by J. F. Clauser, M. A. Horne, A. Shimony and R. A. Holt in “Proposed Experiment to Test Local Hidden-Variable Theories”, Phys. Rev. Lett. 23 (1969) 880-884, typically referenced as CHSH. Empirical verification of Bell's inequalities being violated using entangled photons by A. Aspect, P. Grangier and G. Roger in “Experimental Realization of Einstein-Podolsky-Rosen-Bohm Gedanken-experiment: A New Violation of Bell's Inequalities”, Phys. Rev. Lett. 49 (1982) 91-94 demonstrated the absence of hidden-variables and confirmed the existence of non-locality of entangled particles. These developments are summarized by A. Aspect in Nature 398 (1999) 189-190.
Experimental proposals employed discrete parameters, such as spin and/or polarization, rather than continuum quantities, such as momentum. Most experiments designed to test Bell's theorem have been based on polarization of photons, rather than spins of electrons. The empirical confirmation of entanglement (linking properties of spatially separated particles) has led to further developments that exploit this principle in quantum mechanics, including advances in interferometry.
Interferometry provides the technique of using an interference pattern created by the superposition of two or more waves to diagnose the properties of the aforementioned waves. (It should be noted that a photon has an associated quantum mechanical wave.) The instrument used to interfere the waves together is called an interferometer. Typically, a single incoming beam of light is split into two identical beams by a grating or a partial mirror. Each of these beams will travel a different route, called a path, before they are recombined at a second beam-splitter. An accurate superposition of the two outgoing beams from the second beam-splitter creates an interference pattern. The path distance traveled by each beam creates a phase difference between them. This phase difference shifts the interference pattern between initially identical waves to indicate a phase shift along the paths, such a phase shift can occur due to a change in refractive index and/or path length.
In particular, a Mach-Zehnder Interferometer (MZI) can be used to determine phase shift in a sample object within the path of one of two collimated beams having planar wave-fronts from a coherent light source, such as a laser. A collimated source beam is split by a half-silvered mirror into two resulting beams: a “sample beam” and a “reference beam”, each is then reflected by a fully-silvered mirror. The “sample beam” passes through an object that is inserted during one experimental run and removed during another experimental run, whereas the “reference beam” does not have any objects inserted or removed for the experimental runs. The two beams then pass a second half-silvered mirror.
Transmission through the sample medium reduces the light velocity to v=c/n, where c is light speed in vacuum and n is the medium's index of refraction, thereby causing a phase shift proportional to the difference in the medium's refractive index (from the displaced medium's refractive index) multiplied by the distance traveled. In the absence of the object, interference profile can be determined. By contrast, a sample object placed in the path of the sample beam changes the position of the interference profile, enabling the resulting phase shift to be calculated.
Three-wave mixing is the process involving a pump beam, signal beam, and idler beam. For the sake of simplicity, the degenerate case is assumed throughout this disclosure. The degenerate case is when the signal and idler beam have the same angular frequency. The higher energy pump photon can generate two lower energy photons, or the two lower energy photons can generate one high energy pump photon. Both processes are reversible. Thus, the down-conversion can be followed by an up-conversion in the same crystal or by a subsequent similar crystal. The bandwidth of the pump beam is typically smaller than the bandwidths of either signal or idler beams, and pulse lasers are employed for the two-photon absorptive switch for this reason. The optical bandwidth of a pulse laser is generally larger than the optical bandwidth of a continuous-wave (cw) laser.
Thus, one can more easily match the signal and idler bandwidths equal to the pump bandwidth with optical bandwidth filters. This bandwidth matching is needed for a two-photon absorption (TPA) switch. That is, bandwidth matching is a requirement for the reversibility between the down-conversion and up-conversion processes. Filters can be placed in front of any detector or detection process to fulfill this requirement. Two-particle absorption (TPA) represents the simultaneous absorption of two photons in order to excite a molecule from one state (such as ground) to a higher-energy state. Generally, TPA provides a non-linear effect in a two-stage process: first to induce the crystal bonds to behave non-linearly, and second to comply with conservation (e.g., momentum conservation or phase-matching). The first stage can be understood by analogizing the crystal atoms and their bond-like masses connected together by springs.
Within the linear domain, stretch of the spring obeys Hooke's law. Hence, for masses set in motion at some driving angular frequency ω, the masses would continue to vibrate at the angular frequency ω after release of the driver. The electric field in a light-wave moves past a point in a crystal at angular frequency ω, thereby causing a charged mass to vibrate at the angular frequency ω. The charged masses collectively reradiate the light in the same direction and with the same ω vibration. This description is a classical view of light moving through a linear material. However, for springs that are sufficiently stretched, the masses would continue to vibrate at ω, but could also vibrate at 2ω, or anharmonically. This description is a classical view of intense light moving through a non-linear material. Because light is quantized into “photons”, the particle picture would suggest that two low-energy photons at angular frequency ω could be combined into one high energy photon at 2ω. By this classical analogy, particle illustration for TPA emerges.
The susceptibility is a constant of proportionality that is multiplied by the electric field strength to obtain the macroscopically averaged electric dipole of a medium, if the material is in the linear domain when the dipoles behave harmonically. However, the incident light can become sufficiently intense, without disassociating the dipoles, so that the dipoles behave anharmonically. In this domain, non-linear susceptibilities may appear. These susceptibilities are based upon symmetry or anti-symmetry properties of the material. Typically, crystals can have even-order non-linear susceptibilities of which the second-order is dominant. Alternatively, certain amorphous materials, can have odd-order non-linear susceptibilities of which the third-order is dominant. This disclosure mainly describes the second-order non-linearity. Generation of two low-energy photons from one high-energy photon for the purpose of generating a “two-photon” quantum state often employs a non-linear, non-centro-symmetric crystal, also known as a χ(2) crystal.
Quantum optics employs parametric down-conversion of photons. Under Spontaneous parametric down-conversion (SPDC), a non-linear crystal splits an incoming photon into a pair of photons of lower energy—called “signal” and “idler” photons—whose combined energy and momentum equals those of the original photon, leaving the state of the crystal unchanged under conservation laws.
Photon conversion can be referenced between three photons as the pump→signal+idler, in a down-conversion and signal+idler→pump in an up-conversion. Phase-matching dictates entanglement of the photon pair in the frequency domain. Conservation of energy ℏω (Dirac constant multiplied by angular frequency) requires frequencies obey the relation ωp=ωs+ωi, and degeneracy imposes ωs=ωi=½ωp, where subscripts p, s and i respectively denote the pump, signal and idler photons. Conservation of momentum k (a.k.a. phase-matching) requires the momenta vectors obey the relation kp=ks+ki.
SPDC creates the photon pairs at random intervals. Detection of one (signal) indicates presence of the other (idler) photon. Polarization between the signal and idler photons is the same for type I, or else is perpendicular to each other for type II. SPDC enables creation of optical fields containing (approximately) a single photon, also known as a Fock state. The Fock state has a well-defined number of particles in each state. For simplicity, a single mode (e.g., a harmonic oscillator) has a Fock state of the type |n with n being an integer value, meaning that there are n quanta of excitation in the mode. A ground state (i.e., having no photons) corresponds to type |0.
Bra-ket notation was created by Paul A. M. Dirac to describe quantum states in quantum mechanics. The inner (or dot) product of two states φ and ψ is denoted by a bracket, φ|ψ, consisting of a left part, φ|, called the “bra” for the φ state, and a right part, |ψ, called the “ket” for the ψ state. In quantum mechanics, the expression φ|ψ that represents the coefficient for the projection of ψ onto φ is typically interpreted as the probability amplitude for the state to collapse ψ into the state φ.
The ket can be expressed as a column vector such as for a discrete representation of the wave-function (or state), |ψ=(c0, c1, c2, . . . )T with c representing complex coefficients. (In infinite-dimensional spaces, the ket may be written in complex function notation, by pre-pending it with a bra, such as in example, x|ψ=ψ(x)=ce−ikx.) Every ket |ψ has a dual counterpart called bra, written as ψ|. For example, the bra corresponding to the ket |ψ above would be the row vector ψ|=(c0*, c1*, c2*, . . . ).
A given wave-function (or state) of a particle can be represented, in a discrete representation of the wave-function (or state), by a ket as earlier shown. For two particles, a separable product of kets can be made when the state of one particle does not imply the state of another particle. However, for two-entangled particles, a separable product of kets can not be made, because the state of one particle implies the state of the other particle. Bell states, as described later, are such non-separable states.